Some distribution results of the Oppenheim continued fractions (Q1675294)

In this paper, the authors are mainly concerned with the distribution properties of the Oppenheim continued fraction expansions. The first result is a Gauss-Kuzumin-Lévy type theorem, which is concerned with the conditional distribution function as well as its conditional density with respect to the basic intervals. The second result deals with the asymptotic distribution of the sequence of partial maxima of some stationary process in extreme value theory. This result shows a Fréchet law concerning this type, extending previous work of \textit{J. Galambos} [Q. J. Math., Oxf. II. Ser. 23, 147--151 (1972; Zbl 0234.10041)] and \textit{W. Philipp} [Acta Arith. 28, 379--386 (1976; Zbl 0332.10033)] on the regular continued fraction expansion. The third result concerns a uniform distribution modulo \(1\).